A new Mustang is starting to look really nice....
I dunno, I remember carrying a rope in my old Mustang because of the
same problem you're having! Had to tie between the doors to hold the
driver's door shut for most of a week, then it thawed out.
I'd say to take a heat gun or hair dryer to the latch itself and work
the cogs/lever until it'll click. If it won't then it sounds like the spring
for the latching dog is broken.
If it's frozen then it might be in order to glue a piece of milk carton or
something over the top (inside the door) to shield it from water coming
down between the glass and the squeegee. Unless there's an easy
way to seal it up.
Loren